TUYMAADA 1995 Problem 4

It is known that the merchant's $n$ clients live in locations laid along the ring road. Of these, $k$ customers have debts to the merchant for $a_1,a_2,...,a_k$ rubles, and the merchant owes the remaining $n-k$ clients, whose debts are $b_1,b_2,...,b_{n-k}$ rubles, moreover, $a_1+a_2+...+a_k=b_1+b_2+...+b_{n-k}$ . Prove that a merchant who has no money can pay all his debts and have paid all the customer debts, by starting a customer walk along the road from one of points and not missing any of their customers.